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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.linear;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.util.ExceptionContext;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.IterationManager;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * &lt;p&gt;<a name="line.26"></a>
<FONT color="green">027</FONT>     * This is an implementation of the conjugate gradient method for<a name="line.27"></a>
<FONT color="green">028</FONT>     * {@link RealLinearOperator}. It follows closely the template by &lt;a<a name="line.28"></a>
<FONT color="green">029</FONT>     * href="#BARR1994"&gt;Barrett et al. (1994)&lt;/a&gt; (figure 2.5). The linear system at<a name="line.29"></a>
<FONT color="green">030</FONT>     * hand is A &amp;middot; x = b, and the residual is r = b - A &amp;middot; x.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;/p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;h3&gt;&lt;a id="stopcrit"&gt;Default stopping criterion&lt;/a&gt;&lt;/h3&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * A default stopping criterion is implemented. The iterations stop when || r ||<a name="line.34"></a>
<FONT color="green">035</FONT>     * &amp;le; &amp;delta; || b ||, where b is the right-hand side vector, r the current<a name="line.35"></a>
<FONT color="green">036</FONT>     * estimate of the residual, and &amp;delta; a user-specified tolerance. It should<a name="line.36"></a>
<FONT color="green">037</FONT>     * be noted that r is the so-called &lt;em&gt;updated&lt;/em&gt; residual, which might<a name="line.37"></a>
<FONT color="green">038</FONT>     * differ from the true residual due to rounding-off errors (see e.g. &lt;a<a name="line.38"></a>
<FONT color="green">039</FONT>     * href="#STRA2002"&gt;Strakos and Tichy, 2002&lt;/a&gt;).<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;h3&gt;Iteration count&lt;/h3&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     * &lt;p&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * In the present context, an iteration should be understood as one evaluation<a name="line.43"></a>
<FONT color="green">044</FONT>     * of the matrix-vector product A &amp;middot; x. The initialization phase therefore<a name="line.44"></a>
<FONT color="green">045</FONT>     * counts as one iteration.<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;/p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;h3&gt;&lt;a id="context"&gt;Exception context&lt;/a&gt;&lt;/h3&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;p&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * Besides standard {@link DimensionMismatchException}, this class might throw<a name="line.49"></a>
<FONT color="green">050</FONT>     * {@link NonPositiveDefiniteOperatorException} if the linear operator or<a name="line.50"></a>
<FONT color="green">051</FONT>     * the preconditioner are not positive definite. In this case, the<a name="line.51"></a>
<FONT color="green">052</FONT>     * {@link ExceptionContext} provides some more information<a name="line.52"></a>
<FONT color="green">053</FONT>     * &lt;ul&gt;<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;li&gt;key {@code "operator"} points to the offending linear operator, say L,&lt;/li&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * &lt;li&gt;key {@code "vector"} points to the offending vector, say x, such that<a name="line.55"></a>
<FONT color="green">056</FONT>     * x&lt;sup&gt;T&lt;/sup&gt; &amp;middot; L &amp;middot; x &lt; 0.&lt;/li&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;/ul&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * &lt;/p&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>     * &lt;h3&gt;References&lt;/h3&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * &lt;dl&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * &lt;dt&gt;&lt;a id="BARR1994"&gt;Barret et al. (1994)&lt;/a&gt;&lt;/dt&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>     * &lt;dd&gt;R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra,<a name="line.62"></a>
<FONT color="green">063</FONT>     * V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst,<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;a href="http://www.netlib.org/linalg/html_templates/Templates.html"&gt;&lt;em&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     * Templates for the Solution of Linear Systems: Building Blocks for Iterative<a name="line.65"></a>
<FONT color="green">066</FONT>     * Methods&lt;/em&gt;&lt;/a&gt;, SIAM&lt;/dd&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;dt&gt;&lt;a id="STRA2002"&gt;Strakos and Tichy (2002)<a name="line.67"></a>
<FONT color="green">068</FONT>     * &lt;dt&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     * &lt;dd&gt;Z. Strakos and P. Tichy, &lt;a<a name="line.69"></a>
<FONT color="green">070</FONT>     * href="http://etna.mcs.kent.edu/vol.13.2002/pp56-80.dir/pp56-80.pdf"&gt;<a name="line.70"></a>
<FONT color="green">071</FONT>     * &lt;em&gt;On error estimation in the conjugate gradient method and why it works<a name="line.71"></a>
<FONT color="green">072</FONT>     * in finite precision computations&lt;/em&gt;&lt;/a&gt;, Electronic Transactions on<a name="line.72"></a>
<FONT color="green">073</FONT>     * Numerical Analysis 13: 56-80, 2002&lt;/dd&gt;<a name="line.73"></a>
<FONT color="green">074</FONT>     * &lt;/dl&gt;<a name="line.74"></a>
<FONT color="green">075</FONT>     *<a name="line.75"></a>
<FONT color="green">076</FONT>     * @version $Id: ConjugateGradient.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.76"></a>
<FONT color="green">077</FONT>     * @since 3.0<a name="line.77"></a>
<FONT color="green">078</FONT>     */<a name="line.78"></a>
<FONT color="green">079</FONT>    public class ConjugateGradient<a name="line.79"></a>
<FONT color="green">080</FONT>        extends PreconditionedIterativeLinearSolver {<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>        /** Key for the &lt;a href="#context"&gt;exception context&lt;/a&gt;. */<a name="line.82"></a>
<FONT color="green">083</FONT>        public static final String OPERATOR = "operator";<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>        /** Key for the &lt;a href="#context"&gt;exception context&lt;/a&gt;. */<a name="line.85"></a>
<FONT color="green">086</FONT>        public static final String VECTOR = "vector";<a name="line.86"></a>
<FONT color="green">087</FONT>    <a name="line.87"></a>
<FONT color="green">088</FONT>        /**<a name="line.88"></a>
<FONT color="green">089</FONT>         * {@code true} if positive-definiteness of matrix and preconditioner should<a name="line.89"></a>
<FONT color="green">090</FONT>         * be checked.<a name="line.90"></a>
<FONT color="green">091</FONT>         */<a name="line.91"></a>
<FONT color="green">092</FONT>        private boolean check;<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>        /** The value of &amp;delta;, for the default stopping criterion. */<a name="line.94"></a>
<FONT color="green">095</FONT>        private final double delta;<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>        /**<a name="line.97"></a>
<FONT color="green">098</FONT>         * Creates a new instance of this class, with &lt;a href="#stopcrit"&gt;default<a name="line.98"></a>
<FONT color="green">099</FONT>         * stopping criterion&lt;/a&gt;.<a name="line.99"></a>
<FONT color="green">100</FONT>         *<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param maxIterations the maximum number of iterations<a name="line.101"></a>
<FONT color="green">102</FONT>         * @param delta the &amp;delta; parameter for the default stopping criterion<a name="line.102"></a>
<FONT color="green">103</FONT>         * @param check {@code true} if positive definiteness of both matrix and<a name="line.103"></a>
<FONT color="green">104</FONT>         * preconditioner should be checked<a name="line.104"></a>
<FONT color="green">105</FONT>         */<a name="line.105"></a>
<FONT color="green">106</FONT>        public ConjugateGradient(final int maxIterations, final double delta,<a name="line.106"></a>
<FONT color="green">107</FONT>                                 final boolean check) {<a name="line.107"></a>
<FONT color="green">108</FONT>            super(maxIterations);<a name="line.108"></a>
<FONT color="green">109</FONT>            this.delta = delta;<a name="line.109"></a>
<FONT color="green">110</FONT>            this.check = check;<a name="line.110"></a>
<FONT color="green">111</FONT>        }<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>        /**<a name="line.113"></a>
<FONT color="green">114</FONT>         * Creates a new instance of this class, with &lt;a href="#stopcrit"&gt;default<a name="line.114"></a>
<FONT color="green">115</FONT>         * stopping criterion&lt;/a&gt; and custom iteration manager.<a name="line.115"></a>
<FONT color="green">116</FONT>         *<a name="line.116"></a>
<FONT color="green">117</FONT>         * @param manager the custom iteration manager<a name="line.117"></a>
<FONT color="green">118</FONT>         * @param delta the &amp;delta; parameter for the default stopping criterion<a name="line.118"></a>
<FONT color="green">119</FONT>         * @param check {@code true} if positive definiteness of both matrix and<a name="line.119"></a>
<FONT color="green">120</FONT>         * preconditioner should be checked<a name="line.120"></a>
<FONT color="green">121</FONT>         * @throws NullArgumentException if {@code manager} is {@code null}<a name="line.121"></a>
<FONT color="green">122</FONT>         */<a name="line.122"></a>
<FONT color="green">123</FONT>        public ConjugateGradient(final IterationManager manager,<a name="line.123"></a>
<FONT color="green">124</FONT>                                 final double delta, final boolean check)<a name="line.124"></a>
<FONT color="green">125</FONT>            throws NullArgumentException {<a name="line.125"></a>
<FONT color="green">126</FONT>            super(manager);<a name="line.126"></a>
<FONT color="green">127</FONT>            this.delta = delta;<a name="line.127"></a>
<FONT color="green">128</FONT>            this.check = check;<a name="line.128"></a>
<FONT color="green">129</FONT>        }<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>        /**<a name="line.131"></a>
<FONT color="green">132</FONT>         * Returns {@code true} if positive-definiteness should be checked for both<a name="line.132"></a>
<FONT color="green">133</FONT>         * matrix and preconditioner.<a name="line.133"></a>
<FONT color="green">134</FONT>         *<a name="line.134"></a>
<FONT color="green">135</FONT>         * @return {@code true} if the tests are to be performed<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        public final boolean getCheck() {<a name="line.137"></a>
<FONT color="green">138</FONT>            return check;<a name="line.138"></a>
<FONT color="green">139</FONT>        }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        /**<a name="line.141"></a>
<FONT color="green">142</FONT>         * {@inheritDoc}<a name="line.142"></a>
<FONT color="green">143</FONT>         *<a name="line.143"></a>
<FONT color="green">144</FONT>         * @throws NonPositiveDefiniteOperatorException if {@code a} or {@code m} is<a name="line.144"></a>
<FONT color="green">145</FONT>         * not positive definite<a name="line.145"></a>
<FONT color="green">146</FONT>         */<a name="line.146"></a>
<FONT color="green">147</FONT>        @Override<a name="line.147"></a>
<FONT color="green">148</FONT>        public RealVector solveInPlace(final RealLinearOperator a,<a name="line.148"></a>
<FONT color="green">149</FONT>                                       final RealLinearOperator m,<a name="line.149"></a>
<FONT color="green">150</FONT>                                       final RealVector b,<a name="line.150"></a>
<FONT color="green">151</FONT>                                       final RealVector x0)<a name="line.151"></a>
<FONT color="green">152</FONT>            throws NullArgumentException, NonPositiveDefiniteOperatorException,<a name="line.152"></a>
<FONT color="green">153</FONT>            NonSquareOperatorException, DimensionMismatchException,<a name="line.153"></a>
<FONT color="green">154</FONT>            MaxCountExceededException, NonPositiveDefiniteOperatorException {<a name="line.154"></a>
<FONT color="green">155</FONT>            checkParameters(a, m, b, x0);<a name="line.155"></a>
<FONT color="green">156</FONT>            final IterationManager manager = getIterationManager();<a name="line.156"></a>
<FONT color="green">157</FONT>            // Initialization of default stopping criterion<a name="line.157"></a>
<FONT color="green">158</FONT>            manager.resetIterationCount();<a name="line.158"></a>
<FONT color="green">159</FONT>            final double rmax = delta * b.getNorm();<a name="line.159"></a>
<FONT color="green">160</FONT>            final RealVector bro = RealVector.unmodifiableRealVector(b);<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>            // Initialization phase counts as one iteration.<a name="line.162"></a>
<FONT color="green">163</FONT>            manager.incrementIterationCount();<a name="line.163"></a>
<FONT color="green">164</FONT>            // p and x are constructed as copies of x0, since presumably, the type<a name="line.164"></a>
<FONT color="green">165</FONT>            // of x is optimized for the calculation of the matrix-vector product<a name="line.165"></a>
<FONT color="green">166</FONT>            // A.x.<a name="line.166"></a>
<FONT color="green">167</FONT>            final RealVector x = x0;<a name="line.167"></a>
<FONT color="green">168</FONT>            final RealVector xro = RealVector.unmodifiableRealVector(x);<a name="line.168"></a>
<FONT color="green">169</FONT>            final RealVector p = x.copy();<a name="line.169"></a>
<FONT color="green">170</FONT>            RealVector q = a.operate(p);<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>            final RealVector r = b.combine(1, -1, q);<a name="line.172"></a>
<FONT color="green">173</FONT>            final RealVector rro = RealVector.unmodifiableRealVector(r);<a name="line.173"></a>
<FONT color="green">174</FONT>            double rnorm = r.getNorm();<a name="line.174"></a>
<FONT color="green">175</FONT>            RealVector z;<a name="line.175"></a>
<FONT color="green">176</FONT>            if (m == null) {<a name="line.176"></a>
<FONT color="green">177</FONT>                z = r;<a name="line.177"></a>
<FONT color="green">178</FONT>            } else {<a name="line.178"></a>
<FONT color="green">179</FONT>                z = null;<a name="line.179"></a>
<FONT color="green">180</FONT>            }<a name="line.180"></a>
<FONT color="green">181</FONT>            IterativeLinearSolverEvent evt;<a name="line.181"></a>
<FONT color="green">182</FONT>            evt = new DefaultIterativeLinearSolverEvent(this,<a name="line.182"></a>
<FONT color="green">183</FONT>                manager.getIterations(), xro, bro, rro, rnorm);<a name="line.183"></a>
<FONT color="green">184</FONT>            manager.fireInitializationEvent(evt);<a name="line.184"></a>
<FONT color="green">185</FONT>            if (rnorm &lt;= rmax) {<a name="line.185"></a>
<FONT color="green">186</FONT>                manager.fireTerminationEvent(evt);<a name="line.186"></a>
<FONT color="green">187</FONT>                return x;<a name="line.187"></a>
<FONT color="green">188</FONT>            }<a name="line.188"></a>
<FONT color="green">189</FONT>            double rhoPrev = 0.;<a name="line.189"></a>
<FONT color="green">190</FONT>            while (true) {<a name="line.190"></a>
<FONT color="green">191</FONT>                manager.incrementIterationCount();<a name="line.191"></a>
<FONT color="green">192</FONT>                evt = new DefaultIterativeLinearSolverEvent(this,<a name="line.192"></a>
<FONT color="green">193</FONT>                    manager.getIterations(), xro, bro, rro, rnorm);<a name="line.193"></a>
<FONT color="green">194</FONT>                manager.fireIterationStartedEvent(evt);<a name="line.194"></a>
<FONT color="green">195</FONT>                if (m != null) {<a name="line.195"></a>
<FONT color="green">196</FONT>                    z = m.operate(r);<a name="line.196"></a>
<FONT color="green">197</FONT>                }<a name="line.197"></a>
<FONT color="green">198</FONT>                final double rhoNext = r.dotProduct(z);<a name="line.198"></a>
<FONT color="green">199</FONT>                if (check &amp;&amp; (rhoNext &lt;= 0.)) {<a name="line.199"></a>
<FONT color="green">200</FONT>                    final NonPositiveDefiniteOperatorException e;<a name="line.200"></a>
<FONT color="green">201</FONT>                    e = new NonPositiveDefiniteOperatorException();<a name="line.201"></a>
<FONT color="green">202</FONT>                    final ExceptionContext context = e.getContext();<a name="line.202"></a>
<FONT color="green">203</FONT>                    context.setValue(OPERATOR, m);<a name="line.203"></a>
<FONT color="green">204</FONT>                    context.setValue(VECTOR, r);<a name="line.204"></a>
<FONT color="green">205</FONT>                    throw e;<a name="line.205"></a>
<FONT color="green">206</FONT>                }<a name="line.206"></a>
<FONT color="green">207</FONT>                if (manager.getIterations() == 2) {<a name="line.207"></a>
<FONT color="green">208</FONT>                    p.setSubVector(0, z);<a name="line.208"></a>
<FONT color="green">209</FONT>                } else {<a name="line.209"></a>
<FONT color="green">210</FONT>                    p.combineToSelf(rhoNext / rhoPrev, 1., z);<a name="line.210"></a>
<FONT color="green">211</FONT>                }<a name="line.211"></a>
<FONT color="green">212</FONT>                q = a.operate(p);<a name="line.212"></a>
<FONT color="green">213</FONT>                final double pq = p.dotProduct(q);<a name="line.213"></a>
<FONT color="green">214</FONT>                if (check &amp;&amp; (pq &lt;= 0.)) {<a name="line.214"></a>
<FONT color="green">215</FONT>                    final NonPositiveDefiniteOperatorException e;<a name="line.215"></a>
<FONT color="green">216</FONT>                    e = new NonPositiveDefiniteOperatorException();<a name="line.216"></a>
<FONT color="green">217</FONT>                    final ExceptionContext context = e.getContext();<a name="line.217"></a>
<FONT color="green">218</FONT>                    context.setValue(OPERATOR, a);<a name="line.218"></a>
<FONT color="green">219</FONT>                    context.setValue(VECTOR, p);<a name="line.219"></a>
<FONT color="green">220</FONT>                    throw e;<a name="line.220"></a>
<FONT color="green">221</FONT>                }<a name="line.221"></a>
<FONT color="green">222</FONT>                final double alpha = rhoNext / pq;<a name="line.222"></a>
<FONT color="green">223</FONT>                x.combineToSelf(1., alpha, p);<a name="line.223"></a>
<FONT color="green">224</FONT>                r.combineToSelf(1., -alpha, q);<a name="line.224"></a>
<FONT color="green">225</FONT>                rhoPrev = rhoNext;<a name="line.225"></a>
<FONT color="green">226</FONT>                rnorm = r.getNorm();<a name="line.226"></a>
<FONT color="green">227</FONT>                evt = new DefaultIterativeLinearSolverEvent(this,<a name="line.227"></a>
<FONT color="green">228</FONT>                    manager.getIterations(), xro, bro, rro, rnorm);<a name="line.228"></a>
<FONT color="green">229</FONT>                manager.fireIterationPerformedEvent(evt);<a name="line.229"></a>
<FONT color="green">230</FONT>                if (rnorm &lt;= rmax) {<a name="line.230"></a>
<FONT color="green">231</FONT>                    manager.fireTerminationEvent(evt);<a name="line.231"></a>
<FONT color="green">232</FONT>                    return x;<a name="line.232"></a>
<FONT color="green">233</FONT>                }<a name="line.233"></a>
<FONT color="green">234</FONT>            }<a name="line.234"></a>
<FONT color="green">235</FONT>        }<a name="line.235"></a>
<FONT color="green">236</FONT>    }<a name="line.236"></a>




























































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